Journal of the Association for Computing Machinery, Vol. 42, No. 5, September 1995 (To appear)

A Class of Logic Problems Solvable by Linear Programming

MICHEL CONFORTI

AND

GÉRARD CORNUÉJOLS

Abstract. In propositional logic, several problems, such as satisfiability, MAX SAT and logical inference, can be formulated as integer programs. In this paper, we consider sets of clauses for which the corresponding integer programs can be solved as linear programs. We prove that balanced sets of clauses have this property.

Categories and Subject Descriptors. F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems—computations on discrete structures; G.2.1 [Discrete Mathematics]: Combinatorics—combinatorial algorithms

General Terms. Algorithms

Additional Key words and Phrases. Balanced matrices, linear programming, propositional logic

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